Exact Formulation of Moments for Density of States on Multisite Correlation Function under Constant Composition

Abstract

For a classical discrete system on a periodic lattice under a constant composition, we show that the multivariate any-order moment for the configurational density of states (CDOS) before applying potential energy can be exactly expressed as a linear combination of noncentral 1st-order moments (i.e., average) for a multimember cluster with function F. We here formulate exact multivariate low-order moments by estimating the value of F on the basis of the high temperature expansion in the magnetic system (i.e., variable composition) and confirm the validity of this approach by numerical simulations considering all atomic configurations. These exact multivariate low-order moments are important in that they correspond to the structures of a special microscopic state characterizing the macroscopic property in an equilibrium state.